Followup to:  Probability is Subjectively Objective, Can Counterfactuals Be True?

I am quite confident that the statement 2 + 3 = 5 is true; I am far less confident of what it means for a mathematical statement to be true.

In "The Simple Truth" I defined a pebble-and-bucket system for tracking sheep, and defined a condition for whether a bucket's pebble level is "true" in terms of the sheep.  The bucket is the belief, the sheep are the reality.  I believe 2 + 3 = 5.  Not just that two sheep plus three sheep equal five sheep, but that 2 + 3 = 5.  That is my belief, but where is the reality?

So now the one comes to me and says:  "Yes, two sheep plus three sheep equals five sheep, and two stars plus three stars equals five stars.  I won't deny that.  But this notion that 2 + 3 = 5, exists only in your imagination, and is purely subjective."

Followup to:  The Rhythm of Disagreement

At the age of 15, a year before I knew what a "Singularity" was, I had learned about evolutionary psychology.  Even from that beginning, it was apparent to me that people talked about "disagreement" as a matter of tribal status, processing it with the part of their brain that assessed people's standing in the tribe.  The peculiar indignation of "How dare you disagree with Einstein?" has its origins here:  Even if the disagreer is wrong, we wouldn't apply the same emotions to an ordinary math error like "How dare you write a formula that makes e equal to 1.718?"

At the age of 15, being a Traditional Rationalist, and never having heard of Aumann or Bayes, I thought the obvious answer was, "Entirely disregard people's authority and pay attention to the arguments.  Only arguments count."

Ha ha!  How naive.

Followup to:  Science Doesn't Trust Your Rationality, Einstein's Arrogance

I sometimes say that the method of science is to amass such an enormous mountain of evidence that even scientists cannot ignore it; and that this is the distinguishing characteristic of a scientist, a non-scientist will ignore it anyway.

Max Planck was even less optimistic:

"A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it."

I am much tickled by this notion, because it implies that the power of science to distinguish truth from falsehood ultimately rests on the good taste of grad students.

The gradual increase in acceptance of many-worlds in academic physics, suggests that there are physicists who will only accept a new idea given some combination of epistemic justification, and a sufficiently large academic pack in whose company they can be comfortable.  As more physicists accept, the pack grows larger, and hence more people go over their individual thresholds for conversion—with the epistemic justification remaining essentially the same.

But Science still gets there eventually, and this is sufficient for the ratchet of Science to move forward, and raise up a technological civilization.

Scientists can be moved by groundless prejudices, by undermined intuitions, by raw herd behavior—the panoply of human flaws.  Each time a scientist shifts belief for epistemically unjustifiable reasons, it requires more evidence, or new arguments, to cancel out the noise.

Followup to:  Science Doesn't Trust Your Rationality, Do Scientists Already Know This Stuff?

I don't ask my friends about their childhoods—I lack social curiosity—and so I don't know how much of a trend this really is:

Of the people I know who are reaching upward as rationalists, who volunteer information about their childhoods, there is a surprising tendency to hear things like:  "My family joined a cult and I had to break out," or "One of my parents was clinically insane and I had to learn to filter out reality from their madness."

My own experience with growing up in an Orthodox Jewish family seems tame by comparison... but it accomplished the same outcome:  It broke my core emotional trust in the sanity of the people around me.

Until this core emotional trust is broken, you don't start growing as a rationalist.  I have trouble putting into words why this is so.  Maybe any unusual skills you acquire—anything that makes you unusually rational—requires you to zig when other people zag.  Maybe that's just too scary, if the world still seems like a sane place unto you.

Or maybe you don't bother putting in the hard work to be extra bonus sane, if normality doesn't scare the hell out of you.

Previously in series:  The So-Called Heisenberg Uncertainty Principle

"A human researcher only sees a particle in one place at one time."  At least that's what everyone goes around repeating to themselves.  Personally, I'd say that when a human researcher looks at a quantum computer, they quite clearly see particles not behaving like they're in one place at a time.  In fact, you have never in your life seen a particle "in one place at a time" because they aren't.

Nonetheless, when you construct a big measuring instrument that is sensitive to a particle's location—say, the measuring instrument's behavior depends on whether a particle is to the left or right of some dividing line—then you, the human researcher, see the screen flashing "LEFT", or "RIGHT", but not a mixture like "LIGFT".

As you might have guessed from reading about decoherence and Heisenberg, this is because we ourselves are governed by the laws of quantum mechanics and subject to decoherence.

Followup to:  The So-Called Heisenberg Uncertainty Principle

For decades, quantum physics was vehemently asserted to be nothing but a convenience of calculation.  The equations were not to be interpreted as describing reality, though they made good predictions for reasons that it was mere philosophy to question.  This being the case, any quantity you could define seemed as fundamentally real as any other quantity, which is to say, not real at all.

Physicists have invented, for convenience of calculation, something called a momentum basis of quantum mechanics.  Instead of having a complex amplitude distribution over the positions of particles, you had a complex amplitude distribution over their momenta.

The "momentum basis" contains all the information that is in the "position basis", and the "position basis" contains all the information that is in the "momentum basis".  Physicists use the word "basis" for both, suggesting that they are on the same footing: that positions are no better than momenta, or vice versa.

But, in my humble opinion, the two representations are not on an equal footing when it comes to being "fundamental".

Previously in series:  The Quantum Arena

At this point I would like to introduce another key idea in quantum mechanics.  Unfortunately, this idea was introduced so well in chapter 2 of QED: The Strange Theory of Light and Matter by Richard Feynman, that my mind goes blank when trying to imagine how to introduce it any other way.  As a compromise with just stealing his entire book, I stole one diagram—a diagram of how a mirror really works.

Continuation of:  Zombies! Zombies?

I'm a bit tired today, having stayed up until 3AM writing yesterday's >6000-word post on zombies, so today I'll just reply to Richard, and tie up a loose end I spotted the next day.

Besides, TypePad's nitwit, un-opt-out-able 50-comment pagination "feature", that doesn't work with the Recent Comments sidebar, means that we might as well jump the discussion here before we go over the 50-comment limit.

Followup to:  Expecting Beauty

I was once reading a Robert Heinlein story - sadly I neglected to note down which story, but I do think it was a Heinlein - where one of the characters says something like, "Logic is a fine thing, but I have seen a perfectly logical proof that 2 = 1."  Authors are not to be confused with characters, but the line is voiced by one of Heinlein's trustworthy father figures.  I find myself worried that Heinlein may have meant it.

The classic proof that 2 = 1 runs thus.  First, let x = y = 1.  Then:

1. x  =  y
2. x²  =  xy
3. x² - y²  =  xy - y²
4. (x + y)(x - y)  =  y(x - y)
5. x + y = y
6. 2 = 1

Now, you could look at that, and shrug, and say, "Well, logic doesn't always work."

Or, if you felt that math had rightfully earned just a bit more credibility than that, over the last thirty thousand years, then you might suspect the flaw lay in your use of math, rather than Math Itself.

You might suspect that the proof was not, in fact, "perfectly logical".

The novice goes astray and says:  "The Art failed me."
The master goes astray and says:  "I failed my Art."